Home > Trigonometry > Converting Between Systems

How do you convert #y = sqrt(3)x# into polar form?

Answer 1

Aaliyah Abdullah

Use these identities ...
#x=rcostheta#
#y=rsintheta#

Using substitution , insert the identities above into the equation:

#rsintheta=sqrt3xxrcostheta#

#r(sintheta -sqrt3costheta)=0#

#sintheta=sqrt3costheta#

#tantheta=sqrt3#

#theta=pi/3#

So, polar form is a straight line : #theta = pi/3#

hope that helped

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elijah Alexander

To convert the equation ( y = \sqrt{3}x ) into polar form:

Recognize that in polar form, ( x = r \cos(\theta) ) and ( y = r \sin(\theta) ).
Substitute ( y = r \sin(\theta) ) and ( x = r \cos(\theta) ) into the equation ( y = \sqrt{3}x ).
We get ( r \sin(\theta) = \sqrt{3} r \cos(\theta) ).
Divide both sides by ( r \cos(\theta) ): ( \frac{r \sin(\theta)}{r \cos(\theta)} = \sqrt{3} ).
Simplify: ( \tan(\theta) = \sqrt{3} ).

So, the polar form of the equation ( y = \sqrt{3}x ) is ( \tan(\theta) = \sqrt{3} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.